Subgroups — C₄₃×#20740 #24940757

Order 11008.

1350 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#432	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2285	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1823	C₂	1	2	yes	maximal
5	C₄₃×#1803	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1787	C₂	1	2	yes	maximal
7	C₄₃×#1763	C₂	1	4	yes	maximal, complemented
8	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₄₃	—	2	4	no	—
10	C₂×C₄×Q₈×C₄₃	—	2	1	no	—
11	C₂×C₄×Q₈×C₄₃	—	2	1	no	—
12	C₂×C₄×Q₈×C₄₃	C₄	1	8	yes	complemented
13	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
15	C₂×#117×C₄₃	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₃	—	2	1	no	—
19	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#432	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
22	C₂×#103×C₄₃	C₂²	1	8	yes	—
23	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
24	C₂×#97×C₄₃	C₂²	1	2	yes	—
25	C₄₃×#384	C₂²	1	2	yes	—
26	C₄₃×#382	—	2	1	no	—
27	C₄₃×#380	—	2	1	no	—
28	C₄₃×#380	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
30	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
31	C₄₃×#340	C₂²	1	8	yes	—
32	C₂²×Q₈×C₄₃	—	2	8	no	—
33	C₂²×Q₈×C₄₃	—	2	2	no	—
34	C₂²×Q₈×C₄₃	—	2	1	no	—
35	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	—
36	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₃	—	2	1	no	—
38	C₂³×C₄×C₄₃	—	2	1	no	—
39	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
43	C₄×Q₈×C₄₃	—	2	8	no	—
44	C₄×Q₈×C₄₃	—	2	8	no	—
45	C₄×Q₈×C₄₃	—	2	4	no	—
46	C₄×Q₈×C₄₃	—	2	4	no	—
47	C₄×Q₈×C₄₃	C₂×C₄	1	8	yes	—
48	C₄×Q₈×C₄₃	C₂×C₄	1	8	yes	—
49	#117×C₄₃	—	4	4	no	—
50	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
51	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₄²×C₄₃	—	2	8	no	—
62	C₂×C₄²×C₄₃	—	2	2	no	—
63	C₂×C₄²×C₄₃	—	2	2	no	—
64	C₂×C₄²×C₄₃	—	2	2	no	—
65	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
66	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₃	D₄	1	4	yes	—
69	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₄₃	—	2	4	no	—
72	#103×C₄₃	—	2	16	no	—
73	C₂²⋊C₈×C₄₃	—	2	4	no	—
74	#97×C₄₃	—	2	4	no	—
75	#95×C₄₃	—	2	2	no	—
76	#95×C₄₃	—	2	2	no	—
77	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₄₃	—	2	16	no	—
79	C₂×Q₈×C₄₃	—	2	8	no	—
80	C₂×Q₈×C₄₃	—	2	16	no	—
81	C₂×Q₈×C₄₃	—	2	4	no	—
82	C₂×Q₈×C₄₃	—	2	2	no	—
83	C₂×Q₈×C₄₃	—	2	4	no	—
84	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
85	C₂×Q₈×C₄₃	#41	1	8	yes	—
86	C₂²×C₄×C₄₃	—	2	8	no	—
87	C₂²×C₄×C₄₃	—	2	4	no	—
88	C₂²×C₄×C₄₃	—	2	4	no	—
89	C₂²×C₄×C₄₃	—	2	4	no	—
90	C₂²×C₄×C₄₃	—	2	4	no	—
91	C₂²×C₄×C₄₃	—	2	2	no	—
92	C₂²×C₄×C₄₃	—	2	2	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	2	no	—
95	C₂²×C₄×C₄₃	—	2	4	no	—
96	C₂²×C₄×C₄₃	—	4	2	no	—
97	C₂²×C₄×C₄₃	—	4	2	no	—
98	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
100	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₄₃	—	2	4	no	—
109	C₂×C₈×C₄₃	—	2	8	no	—
110	C₄⋊C₄×C₄₃	—	2	8	no	—
111	C₄⋊C₄×C₄₃	—	2	8	no	—
112	C₄⋊C₄×C₄₃	—	2	4	no	—
113	C₄⋊C₄×C₄₃	—	2	2	no	—
114	C₄⋊C₄×C₄₃	—	2	8	no	—
115	C₄⋊C₄×C₄₃	—	4	4	no	—
116	C₄⋊C₄×C₄₃	—	4	4	no	—
117	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
118	C₂²⋊C₄×C₄₃	—	4	4	no	—
119	C₄²×C₄₃	—	2	8	no	—
120	C₄²×C₄₃	—	2	8	no	—
121	C₄²×C₄₃	—	4	4	no	—
122	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
123	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
124	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
125	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₃	C₂×D₄	1	2	yes	—
127	C₄²×C₄₃	C₂×D₄	1	2	yes	—
128	C₂³×C₄₃	—	2	2	no	—
129	C₂³×C₄₃	—	2	2	no	—
130	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
131	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
132	C₂³×C₄₃	#137	1	2	yes	—
133	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₄₃	—	2	16	no	—
135	Q₈×C₄₃	—	2	4	no	—
136	Q₈×C₄₃	—	2	8	no	—
137	Q₈×C₄₃	#117	1	8	yes	complemented
138	C₂×C₄×C₄₃	—	2	16	no	—
139	C₂×C₄×C₄₃	—	2	4	no	—
140	C₂×C₄×C₄₃	—	2	8	no	—
141	C₂×C₄×C₄₃	—	2	2	no	—
142	C₂×C₄×C₄₃	—	2	1	no	—
143	C₂×C₄×C₄₃	—	2	1	no	—
144	C₂×C₄×C₄₃	—	2	2	no	—
145	C₂×C₄×C₄₃	—	2	1	no	—
146	C₂×C₄×C₄₃	—	2	1	no	—
147	C₂×C₄×C₄₃	—	2	8	no	—
148	C₂×C₄×C₄₃	—	2	4	no	—
149	C₂×C₄×C₄₃	—	2	4	no	—
150	C₂×C₄×C₄₃	—	2	8	no	—
151	C₂×C₄×C₄₃	—	2	4	no	—
152	C₂×C₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	—	4	2	no	—
154	C₂×C₄×C₄₃	—	4	8	no	—
155	C₂×C₄×C₄₃	—	4	4	no	—
156	C₂×C₄×C₄₃	—	4	4	no	—
157	C₂×C₄×C₄₃	—	4	4	no	—
158	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₃	#137	1	4	yes	—
164	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
167	C₈×C₄₃	—	4	4	no	—
168	#20740	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂²×C₄₃	—	2	4	no	—
170	C₂²×C₄₃	—	2	4	no	—
171	C₂²×C₄₃	—	2	2	no	—
172	C₂²×C₄₃	—	2	2	no	—
173	C₂²×C₄₃	#417	1	4	yes	—
174	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
175	C₂²×C₄₃	#525	1	2	yes	—
176	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
177	C₂²×C₄₃	C₂×#137	1	2	yes	—
178	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
179	C₄×C₄₃	—	2	2	no	—
180	C₄×C₄₃	—	2	2	no	—
181	C₄×C₄₃	—	2	2	no	—
182	C₄×C₄₃	—	2	8	no	—
183	C₄×C₄₃	—	2	2	no	—
184	C₄×C₄₃	—	4	4	no	—
185	C₄×C₄₃	—	8	4	no	—
186	C₄×C₄₃	#419	1	4	yes	—
187	C₄×C₄₃	C₂×#117	1	2	yes	—
188	C₄×C₄₃	#525	1	2	yes	—
189	C₂²×C₄×Q₈	C₂×C₄₃	1	1	yes	characteristic
190	C₂×#432	C₂×C₄₃	1	1	yes	characteristic
191	#2285	C₂×C₄₃	1	1	yes	characteristic
192	#1823	C₂×C₄₃	1	2	yes	—
193	#1803	C₂×C₄₃	1	4	yes	complemented
194	#1787	C₂×C₄₃	1	2	yes	—
195	#1763	C₂×C₄₃	1	4	yes	complemented
196	C₂×C₄₃	—	2	4	no	—
197	C₂×C₄₃	#2280	1	1	yes	characteristic
198	C₂×C₄₃	C₂×#419	1	1	yes	characteristic
199	C₂×C₄₃	C₂×#417	1	1	yes	characteristic
200	C₂×C₄₃	#3112	1	2	yes	—
201	C₂×C₄₃	#3113	1	2	yes	—
202	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
203	C₂×C₄×Q₈	—	2	4	no	—
204	C₂×C₄×Q₈	—	2	1	no	—
205	C₂×C₄×Q₈	—	2	1	no	—
206	C₂×C₄×Q₈	C₄×C₄₃	1	8	yes	complemented
207	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	—
208	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	—
209	C₂×#117	—	2	1	no	—
210	C₂²×C₄⋊C₄	—	2	1	no	—
211	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
212	C₂²×C₄²	—	2	1	no	—
213	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
214	#432	—	2	4	no	—
215	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
216	C₂×#103	C₂²×C₄₃	1	8	yes	—
217	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
218	C₂×#97	C₂²×C₄₃	1	2	yes	—
219	#384	C₂²×C₄₃	1	2	yes	—
220	#382	—	2	1	no	—
221	#380	—	2	1	no	—
222	#380	C₂²×C₄₃	1	2	yes	—
223	C₄×C₄⋊C₄	—	2	1	no	—
224	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
225	#340	C₂²×C₄₃	1	8	yes	—
226	C₄₃	#20740	1	1	yes	characteristic, direct product factor, Sylow
227	C₂²×Q₈	—	2	8	no	—
228	C₂²×Q₈	—	2	2	no	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	—
231	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	—	2	1	no	—
234	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
235	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
236	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
238	C₄×Q₈	—	2	8	no	—
239	C₄×Q₈	—	2	8	no	—
240	C₄×Q₈	—	2	4	no	—
241	C₄×Q₈	—	2	4	no	—
242	C₄×Q₈	C₂×C₄×C₄₃	1	8	yes	—
243	C₄×Q₈	C₂×C₄×C₄₃	1	8	yes	—
244	#117	—	4	4	no	—
245	C₂×C₄⋊C₄	—	2	8	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
253	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
254	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₄²	—	2	8	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	—	2	2	no	—
260	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
261	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
262	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
263	C₂×C₄²	D₄×C₄₃	1	4	yes	—
264	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
266	C₄⋊C₈	—	2	4	no	—
267	#103	—	2	16	no	—
268	C₂²⋊C₈	—	2	4	no	—
269	#97	—	2	4	no	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
273	C₂×Q₈	—	2	16	no	—
274	C₂×Q₈	—	2	8	no	—
275	C₂×Q₈	—	2	16	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	C₂²×C₄×C₄₃	1	4	yes	—
280	C₂×Q₈	#41×C₄₃	1	8	yes	—
281	C₂²×C₄	—	2	8	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
294	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
295	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
302	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	8	no	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	4	4	no	—
311	C₄⋊C₄	—	4	4	no	—
312	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
313	C₂²⋊C₄	—	4	4	no	—
314	C₄²	—	2	8	no	—
315	C₄²	—	2	8	no	—
316	C₄²	—	4	4	no	—
317	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
318	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
319	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
320	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
321	C₄²	C₂×D₄×C₄₃	1	2	yes	—
322	C₄²	C₂×D₄×C₄₃	1	2	yes	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
326	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
327	C₂³	#137×C₄₃	1	2	yes	—
328	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
329	Q₈	—	2	16	no	—
330	Q₈	—	2	4	no	—
331	Q₈	—	2	8	no	—
332	Q₈	#117×C₄₃	1	8	yes	complemented
333	C₂×C₄	—	2	16	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	8	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	8	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
354	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
355	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
356	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
357	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
358	C₂×C₄	#137×C₄₃	1	4	yes	—
359	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
361	C₂×C₄	C₂×#41×C₄₃	1	4	yes	—
362	C₈	—	4	4	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	C₄₃×#417	1	4	yes	—
368	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
369	C₂²	C₄₃×#525	1	2	yes	—
370	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
371	C₂²	C₂×#137×C₄₃	1	2	yes	—
372	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	8	no	—
377	C₄	—	2	2	no	—
378	C₄	—	4	4	no	—
379	C₄	—	8	4	no	—
380	C₄	C₄₃×#419	1	4	yes	—
381	C₄	C₂×#117×C₄₃	1	2	yes	—
382	C₄	C₄₃×#525	1	2	yes	—
383	C₂	—	2	4	no	—
384	C₂	C₄₃×#2280	1	1	yes	characteristic
385	C₂	C₂×C₄₃×#419	1	1	yes	characteristic
386	C₂	C₂×C₄₃×#417	1	1	yes	characteristic
387	C₂	C₄₃×#3112	1	2	yes	—
388	C₂	C₄₃×#3113	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂⁴×C₄₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
5. C₄₃×#1803	C₂	semidirect
7. C₄₃×#1763	C₂	semidirect
12. C₂×C₄×Q₈×C₄₃	C₄	semidirect
137. Q₈×C₄₃	#117	semidirect
168. #20740	C₄₃	direct (N × H)
193. #1803	C₂×C₄₃	semidirect
195. #1763	C₂×C₄₃	semidirect
206. C₂×C₄×Q₈	C₄×C₄₃	semidirect
226. C₄₃	#20740	direct (N × H)
332. Q₈	#117×C₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄×Q₈×C₄₃	2
C₂×C₄₃×#432	2
C₄₃×#2285	2
C₄₃×#1823	2
C₄₃×#1803	2
C₄₃×#1787	2
C₄₃×#1763	2
#20740	43

Subgroups — C43×#20740 #24940757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20740 #24940757